PSTAT 120A
Probability & Statistics I: Introduction to Probability
Welcome to CLAS / PSTAT 120A Study Page!
We have uploaded by-topic notes on various topics of PSTAT 120A, including 88 practice problems, each with detailed solutions. We also have 5 practice midterms and 7 practice finals to help you prepare for exams! Please come to CLAS weekly group session and drop-in office hours if you have any questions.
1: Set Theory / Calculus ReviewÂ
Topics:Â
1. Basic Set Theory: union/intersection/complement, countable vs. uncountable, De Morgan's law, partition, ...
2. Calculus Review: function basics, derivatives and integrals, geometric series, Taylor series expansion, ...
Calculus Review Practice Problem: 1.1 ~ 1.14
2: Axioms of Probability
Topics: Three axioms of probability and consequences of the axioms: monotonicity, complement, law of total probability, ...
Axioms of Probability Practice Problem: 2.1 ~ 2.10
3: Conditional Probability
Topics: Conditional Probability, Bayes' Rule, Independence and Conditional Independence of Events, ...
Conditional, Bayes, Independence Practice Problem: 3.1 ~ 3.13
4: Random Variables
Topics:Â
1. Random variables: Cumulative distribution functions. Probability mass functions (PMF) for discrete random variables. Probability density functions (PDF) for continuous random variables.
2. Named discrete random variables: Bernoulli, Binomial, Geometric, Hypergeometric, Poisson
Random Variables, PMF/PDF/CDF Practice Problems: 4.1 ~ 4.12
Named Discrete Random Variables Practice Problems: 5.1 ~ 5.7
5: Expected Value and Variance
Topics:
1. Expected value: Expectation of a function of random variables, linearity of expectation, moments, ...
2. Variance: definition and properties.
Expected Value and Variance Practice Problems: 6.1 ~ 6.8
Videos on Named Random Variables
Binomial
Negative Binom
Hypergeometric
Poisson
Uniform
Normal
Exponential
Gamma
6: Moment Generating Functions; Exponential & Normal Distributions
Topics: Moment Generating Functions, Exponential distribution, Normal distribution
Moment Generating Functions Practice Problems: 7.1 ~ 7.6
7: Transformation of Random Variables
Topics: CDF method, Change of Variable Formula, MGF method
8: Joint/Conditional Distribution, Covariance
Topics: Joint distribution of two discrete and continuous random variables. Joint CDF. Expected value of a function of a bivariate random vector. Conditional distribution and conditional expectation. Covariance and correlation.
Joint/Conditional Distribution, Covariance Practice Problems: 8.1 ~ 8.18
9: Limit Theorems
Topics: Markov's Inequality, Chebychev's Inequality, Weak Law of Large Numbers, Central Limit Theorem, Convergence of Random Variables
Practice Finals
Good luck with your finals!
Videos - Extending 120A to 120B
Transformation - PDF Method
Transformation - MGF Method
Gamma integration shortcut
Law of Total Expectation, Variance
UCSB CLAS ECON & STATS